The offered curve to represent a Parabola having vertex at ,(0, -k) which deserve to be obtained by , putting, x=0 and, y+k=0→y= -k.

You are watching: What are the key aspects of the graph of f(x) = x2 – b2, where b is a real number?

→The curve will open vertically Upwards having y axis together Line that Axis.

→It will cut, x axis at two points, if , k0.

→Line, x=0, divides the Parabola right into two equal Parts. The graph the the role is:

f(x)=x² -b²

Here, b is any Real Number.

f(x)=x² - k, where, k=b².

→y+k=x²

The provided curve represents a Parabola having vertex at ,(0, -k) which deserve to be acquired by , putting, x=0 and, y+k=0→y= -k.

→The curve will open up vertically Upwards having y axis as Line of Axis.

→It will cut, x axis at 2 points, if , k0.

→Line, x=0, divides the Parabola right into two same Parts. Given equation is .

Now we must find around what are the an essential aspects of the graph that , where b is a actual number.

We understand that square of any type of number is always positive.

then must be a confident number.

So that means for any type of real number b, together the worth of b rises then graph of f(x) move downward by systems as contrasted to the graph the parent duty

Given equation is .

Now we must find around what are the key aspects of the graph the , wherein b is a real number.

We understand that square of any number is always positive.

then have to be a positive number.

So that means for any real number b, as the value of b rises then graph the f(x) shifts downward by devices as contrasted to the graph of parent duty

The graph has opposite x intercepts of b and also -b. The graph has y intercepts at –b². The graph the the duty symmetrical around the y-axis.

Step-by-step explanation:

Consider the provided graph.

Find the x intercepts by substituting f(x) = 0.   Hence, the x intercepts are b and -b

Now find the y intercepts through substituting x=0.  The graph has y intercepts at –b².

The graph that the provided function is an increase parabola i beg your pardon is symmetrical about the y-axis.

For better understanding to express the figure.

The graph will have actually opposite x-intercepts that b and also –b and also be symmetrical about the y-axis. The graph will have a y-intercept at –b2. No Prob Bob

8⇒

The graph will have opposite x-intercepts the b and also –b and be symmetrical about the y-axis. The graph will have actually a y-intercept at –b2.

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The graph will have opposite x-intercepts of b and also –b and be symmetrical about the y-axis. The graph will have actually a y-intercept at –b2.